Mr Woodhouse said he did not condone any policy that had the effect or appearance of treating one group of people differently from another.
Mr Bush said tonight at Superintendent John Tims of Counties Manukau was looking into how the policy guidelines had been followed in his district.
He said the wording of the policy was inappropriate and would be changed.
"The wording does not reflect the values of the New Zealand Police," he told RNZ.
Nor did it reflect police policy or strategy.
He said there would be no disciplinary action because the guidelines had been issued with the best of intentions.
Maori were over-represented in road deaths and were twice as likely to be killed or injured as others in New Zealand.
Mr Tims told NewstalkZB the document was probably not worded as well as it could be.
"There's two parts to this: the compliance is for everyone, including Maori, and it is about making sure there's less deaths on the road, less crashes."
Maori drivers were "considered" when they were pulled over by police, he said, but were included in the policy simply as part of the Turning the Tide national policy.
PassRite Driving Academy founder Fred Bardon said it was a great way of getting people licensed to drive - but only if it applied it all drivers.
Maori should not be the only targeted group "...because there are other offenders that are doing the same thing and we need to be across the board so that everybody gets the same opportunity", he told NewstalkZB.
Maori health innovator and former New Zealander of the Year Lance O'Sullivan said the policy could help nip downward spirals in the bud.
"You get a kid who gets arrested and then goes to court, then gets fined $500 and can't pay it. There's a spiral of things that we could be responsible for in the first place," he said.
- additional reporting NZME